Question

A planet of radius $R_p$ is revolving around a star of radius $R^{\ast }$, which is at temperature $T^{\ast }$. The distance between the star and the planet is d. If the planet's temperature is $f{T}^{\ast }$, then f is proportional to.

• A. $\sqrt{R^{\ast }/d}$
• B. $R^{\ast }/d$
• C. $R^{\ast }{R}_p/d^2$
• D. $(R^{\ast }/d{)}^4$

Answer 1

The correct option is A $\sqrt{R^{\ast }/d}$

Total energy radiated by star is $\propto$ ${T^{\ast }}^4{R^{\ast }}^2$

Energy received by planet is $\propto$ $\frac{1}{d^2}$

Combining both energy received by planet $\propto$ $(f{T}^{\ast }{)}^4$

$\Rightarrow$ $f^4\propto \frac{{R^{\ast }}^2}{d^2}$

$\Rightarrow f\propto (\frac{{R^{\ast }}^2}{d^2}{)}^{\frac{1}{4}}=\sqrt{\frac{R^{\ast }}{d}}$